Non-hyperbolic correction of seismic data

ABSTRACT

A method for improving seismic images by correction of distortions in the underlying seismic data caused by a near-surface anomaly that produces a non-hyperbolic move-out component of the seismic reflection below the anomaly includes the steps of:
         a. redatuming the input seismic data to go from the surface to a target horizon using true one-way traveltime operators to provide a first new redatuming dataset;   b. redatuming the input seismic data using hyperbolic one-way travel time operators to provide a second new redatuming dataset; and   c. redatuming the combination of a first causal part of the first new redatuming dataset and an anti-causal second part of the second redatuming dataset to go from the target horizon back to the surface using hyperbolic one-way traveltime operators
           to provide a dataset that is referenced to the surface without an imprint of the anomaly.

FIELD OF THE INVENTION

This invention relates to seismic imaging, and in particular to aprocess for the correction of seismic data to minimize the effect ofdistortions caused by a near-surface anomaly that produces anon-hyperbolic move-out in the seismic reflection below that anomaly.

BACKGROUND OF THE INVENTION

A buried velocity anomaly produces a non-hyperbolic move-out in all theseismic reflection events below that anomaly. This non-hyperbolicitydegrades the seismic image after stacking due to the fact that theanomaly imprint cannot be properly described by the stacking velocityfunction or static corrections. This distortion or deterioration canappear as a defocus or as a break in the seismic image.

Conventional time-imaging techniques such as stacking or migration usestacking velocity to describe the nature of seismic data. Stackingvelocity is based on the assumption that all seismic events in thecommon mid-point domain can be described by hyperbolic functions. Inother words, it assumes that the earth's layers in the seismicinvestigation region have very gentle transformations and contain lowrelief structures with minimal lateral velocity changes. However, thisis hardly ever the case with land datasets that suffer from thecomplexities of weathered layers and buried velocity anomalies whichcause the seismic events to be non-hyperbolic.

There are two major families of solutions which are commonly utilized tocompensate for these complexities: statics solutions and redatumingsolutions. In statics solutions, the main underlying assumption is thevertical ray-path assumption which means that a static shift issufficient to remove the effect of the velocity anomaly. That is, asingle value is applied to all of the different time samples of all thetraces that share the same location. However, regardless of the methodused to calculate the static solution, it is valid only if the anomalyis close to the earth's surface, that it is laterally smooth and is lowin velocity. These assumptions don't hold in the case of complexnear-surface or buried velocity anomalies and the static solution cannotaccurately resolve the problem of clarifying the data.

Various methods have been proposed for resolving the problem ofnear-surface anomalies in order to provide more and cleaner data. Forexample, U.S. Pat. No. 6,151,275 discloses a method for separatingseismic data into a first set of seismic data identified as upgoingseismic data, and a second set of seismic data identified as downgoingseismic data. The first and second sets of seismic data are redatumed toa target horizon to provide two sets of seismic data; the new sets arecombined to create an image. Thus, this method tries to first separatethe primaries from the multiples and then stacks them together afteradjusting the datum difference between the two sets. The two sets ofupgoing and downgoing data correspond, respectively to the primaries andfirst order multiples. Since no dataset is produced, it will beunderstood that the ultimate goal of the process described in thispatent is to enhance the produced image by summing the primaries andmultiples in the same image point without returning to the originalsurface of the data.

Redatuming solutions are much more accurate because they resolve theproblem by calculating corrections that are dynamic in time, as well asin offset. One limitation of most redatuming algorithms is that theyrequire the use of knowledge of the velocity-depth model of thenear-surface which is very difficult to obtain in land datasets. Theexception is common focus point (CFP) redatuming which requires onlyknowledge of the one-way traveltime operators to perform the redatuming.Traveltime operators are the one-way time that it takes the wave-fieldto travel from source/receiver point to a reflection point of a targethorizon to which the data will be redatumed. However, CFP redatumingalso has certain limitations, including the following:

-   -   a. the data above the target horizon is degraded because the        redatuming process shifts all the anomalies to those shallower        horizons;    -   b. the new dataset after redatuming has an unknown acquisition        reference in location/depth that is the target horizon; and    -   c. the new dataset after redatuming is different than the input        dataset in reference time, as well as in the move-out behavior        of the seismic events.

CFP-based redatuming is performed using one-way traveltime operatorsfrom the surface to a target horizon. The redatuming process produces adataset which simulates a survey as though the sources and receiverswere positioned at the chosen target horizon. Thus, if the targethorizon is below the buried velocity anomalies, the redatuming processwill shift the chosen imprints of the anomalies from below the targethorizon to above the target horizon, which is referred to as theanti-causal part of the resulting data. The traveltime operators used inCFP redatuming, which are denominated true traveltime operators, exactlydescribe the target horizon in the one-way time domain. This means thatif the data is converted to one-way time, e.g., by creating CFP gathers,or if the operators are converted to two-way time, e.g., by usingFermat's principle, a match should be obtained.

In order to illustrate the limitations of the corrective measures of theprior art methods, reference will be made to the simplified schematicillustration of FIG. 1 where a buried anomaly is positioned at “A”.

It is clear that for a point source at (x, z)=(0, h) and receivers atthe surface, the effect of the buried anomaly will appear on thereceiver from x=xmin to x=xmax, where:

xmin=x0*h/(h−h0) and

xmax=x1*h/(h−h0)

If “d” is the total distance where the effect is measured:

d=xmax−xmin=h*(x1−x0)/(h−h0

However, if h0 is very small or if h is very large, i.e., h>>>h0, then:

xmin=x0 and xmax=x1

It is noted that xmin, xmax and d are dependent on h. This means thatthe effect of the buried velocity anomaly will vary in offset and valueas a function of time. A static solution therefore cannot resolve thiseffect, even if trim statics were used, because of the dynamic nature ofthe problem.

In addition, it will be understood from the above equations that theonly conditions where the effect is not dynamic are when the anomaly isvery shallow or the horizon of interest is very deep. Static correctionswill provide a satisfactory resolution for shallow anomalies; however,as is well known, although static corrections might resolve the problemfor the very deep horizon, it is at the cost of the horizons closer tothe anomaly. Another problem that arises with buried velocity anomaliesis the possibility of having horizons above the anomaly, in which case,it is possible to resolve the problem for the deeper horizons, but theeffect of the anomaly will be imposed on the horizons above it.

Referring to FIG. 2, a simple layered model is illustrated that is 5000m wide with a buried velocity anomaly at x=2500 m. FIG. 3 depicts thereflected events in different CMP gathers which were calculated by raytracing to illustrate the variable effect of the buried anomaly of FIG.2. The common-mid-point (CMP) gathers were taken at x=2300 m, 2400 m and2500 m.

The method of removing the effect of the buried velocity anomaly byCFP-based redatuming utilizes one-way traveltime operators from thesurface to a selected target horizon. Referring to FIG. 4, there isdepicted a simple layered model with a buried anomaly and its CMPgather. The left chart schematically depicts the sources (stars) andreceivers (triangles) at the surface (h0) and a buried velocity anomaly(A) between horizons h1 and h2. The graph to the right depicts theoffset for various CMP gathers. The redatuming process produces adataset which simulates a survey as if sources and receivers werepositioned at that target horizon.

The new dataset will have two parts: a causal part and an anti-causalpart. The causal part shows the reflection coming from below the targethorizon and the anti-causal part shows the reflection coming from abovethe target horizon. In order to remove the effect of a velocity anomalyfrom the deeper horizon, redatuming to any horizon that is below theanomaly is performed.

Referring now to FIG. 5, there is depicted a CMP gather after redatumingwith true traveltime operators. Although the redatuming processsuccessfully removed the anomaly from horizons 3 and 4 in FIG. 5, theredatuming imposed it on the horizons 0 and 1. Another problem is thatthis new dataset differs from the input data in two important ways.First, the new dataset has the target horizon flat at zero, which isconsidered to be undesirable by interpreters of the resultant imagebecause they are used to looking at data from a smoothed surface.Second, the new stacking velocity is very different than the originalstacking velocity, which means that the velocity analysis should berepeated from scratch.

It is therefore an object of the present invention to provide a processfor the correction of seismic data to minimize the effect of distortionscaused by a near-surface anomaly that produces a non-hyperbolic move-outin the seismic reflection below that anomaly.

SUMMARY OF THE INVENTION

The present invention is directed to a novel method that utilizesone-way traveltime operators to provide a correction of the portion ofthe non-hyperbolic seismic data that is attributable to the buriedvelocity anomaly. The method applies three common focus point (CFP)redatuming steps as follows:

-   -   a. one redatuming step on the input seismic data to go from the        surface to a target horizon using true one-way traveltime        operators;    -   b. one redatuming step on the input seismic data to go from the        surface to the target horizon using hyperbolic one-way        traveltime operators; and    -   c. one redatuming step on the combined seismic data, which        consists of the causal part from the first step and the        anti-causal part from the second step, to go from the target        horizon back to the surface using hyperbolic one-way traveltime        operators.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be further described below and the prior art has, tosome extent, been described above with reference to the attacheddrawings in which:

FIG. 1 is a schematic illustration in accordance with the prior art ofthe effect of a buried velocity anomaly;

FIG. 2 is an illustration in accordance with the prior art of a simplelayered model with a buried velocity anomaly;

FIG. 3 are representative graphical plots in accordance with the priorart of common-mid-point gathers for the anomaly of FIG. 2 taken at threedifferent distances;

FIG. 4 includes a schematic illustration in accordance with the priorart of a simple layered model with a buried anomaly on the left and itscorresponding common-mid-point gather to the right;

FIG. 5 includes a schematic illustration in accordance with the priorart of the buried anomaly of FIG. 4 on the left and the correspondingcommon-mid-point gather after redatuming with true traveltime operatorson the right;

FIG. 6 includes a schematic illustration in accordance with the priorart of the buried anomaly of FIG. 4 on the left and the correspondingcommon-mid-point gather after redatuming with hyperbolic traveltimeoperators on the right;

FIG. 7 includes a schematic illustration of the buried anomaly of FIG. 4on the left and the combined common-mid-point gather from two differentredatuming results on the right;

FIG. 8 includes a schematic illustration of the buried anomaly of FIG. 4on the left and the combined common-mid-point gather after redatumingback to the surface with hyperbolic operators;

FIG. 9 is a synthetic velocity model of a specific subsurfacecombination of geophysical features;

FIG. 10 is a surface stack of the model of FIG. 9 before applying thenon-hyperbolic correction method of the present invention;

FIG. 11 is a comparison among a shot, the horizon picks and thehyperbolic correction of the horizon;

FIG. 12 is a comparison of a shot on the left before applying thenon-hyperbolic correction method of the invention and on the right aftersuch correction has been applied;

FIG. 13 is a surface stack after applying the non-hyperbolic correctionmethod of the invention;

FIG. 14 is a comparison of the stacked image before non-hyperboliccorrection on the left side and after correction on the right side forthe indicated time interval;

FIG. 15 is a comparison of the stacked image similar to FIG. 14 for theindicated later time interval;

FIG. 16 is a comparison between horizon velocity analysis at theindicated time before non-hyperbolic correction on the left side andafter correction on the right side; and

FIG. 17 is a comparison of the horizon velocity analysis similar to FIG.16 for the indicated later time.

DETAILED DESCRIPTION OF THE INVENTION

The present invention, which will also be referred to herein as“non-hyperbolic correction” (NHC), uses one-way traveltime operators toachieve non-hyperbolic correction of the seismic data. Each redatumingprocess uses the method of common focus point, or CFP, redatuming.

Hyperbolic Operators

The traveltime operators used in CFP-based redatuming exactly describethe target horizon in one-way time domain. This means that if the datais converted to one-way time e.g., by creating CFP gathers, or if theoperators are converted to two-way time by using Fermat's principle, amatch should be obtained. In accordance with the method of the presentinvention, a new set of operators, referred to as hyperbolic operators,are employed in the redatuming steps. Hyperbolic operators are theone-way time equivalent of the best fitting hyperbolas of the targethorizon in the CMP domain. These hyperbolas are the part of the horizonthat normal move-out (NMO) velocity can properly describe and stack. Inthis context, NMO error is the difference between the actual data andthe best fitting hyperbolas. This error is the cause of thedeterioration and breaking in the stacked image. Note that hyperbolicityin the two-way time domain does not mean hyperbolicity in the one-waytime domain and hyperbolic operators are not themselves hyperbolic.

Hyperbolic operators do not describe the non-hyperbolicity of the buriedvelocity anomaly. If the data is redatumed from the surface to thetarget horizon using these hyperbolic operators, a new dataset isobtained that is similar to the dataset in FIG. 5, except that theanomaly imprint remains in the same horizons, i.e., horizon 3 and 4, andis not shifted to the shallower horizons.

Redatuming Back to the Surface

By comparing FIGS. 5 and 6 which represents the CMP gather afterredatuming with hyperbolic traveltime operators, it can be seen that thegeneral, or hyperbolic, behavior is the same and the only difference isthe location of the anomaly. Also, both the anti-causal part of FIG. 5and the causal part of FIG. 6 do not have the anomaly imprint in them.If the two halves are combined as shown in the combined CMP gather fromtwo different redatuming results of FIG. 7, a dataset is obtained thatdoesn't have the imprint of the anomaly in either the causal or theanti-causal part.

The data is now redatumed back to the surface using the hyperbolicoperators which return the hyperbolic move-out of the behavior withoutintroducing the non-hyperbolic component of the anomaly into any of thehorizons. The result of this process is a dataset which starts from thesurface without the anomaly imprint, as shown in the combined. CMPgather after redatuming back to surface with hyperbolic operators ofFIG. 8. The process of the invention resolves all the issues with theredatumed data at the target horizon that were described above. Theprocess of redatuming with two sets of traveltime operators, combiningthe anomaly-free part of each redatumed dataset and then redatuming backto the surface with the hyperbolic operators is referred to herein asnon-hyperbolic correction (NHC).

Example Using 2D Synthetic Data

An acoustic finite difference algorithm was used to create syntheticshot records for the synthetic velocity model depicted in FIG. 9, whichrepresents a subsurface model containing a wadi, several layers withlateral velocity-variations embedded in the near surface and a number ofsmooth deep reflectors. The sources are located from x=0 m towardsx=10000 m. The shot records are modeled with a moving split-spreadgeometry with an offset range of 4800 m and a source and receiverinterval of 20 m. The synthetic shot records have been processed and ahorizon-consistent velocity analysis was performed to obtain the brutestack of the data shown in FIG. 10 that depicts the surface stack beforeapplying the NHC method of the present invention.

FIG. 10 shows that all the horizons from t=0.8 sec and after appear tobe broken. This is the result of the block-shaped layers visible in FIG.9 at around z=600 m. As noted above, these discontinuities cannot beresolved using static corrections for two reasons: the buried anomaliesare below the first few layers and because the imprint of the anomaliesis dynamic.

Since the velocity analysis was done on this data, the stacking velocityof the target horizon of approximately t=1.05 sec was used as thehyperbolic component of the horizon. A cross-correlation (or trimstatics) was performed in the CMP domain on a short window around thattarget horizon. The cross-correlation results are approximately equal tothe NMO error described above. By adding the stacking velocity to theNMO error, a two-way time picks is obtained of the target horizonincluding all the anomalies' effects. Notice that there are numerousways to get the target horizon picks in the pre-stack domain. As will beunderstood by one of ordinary skill in the art, choosing the best methodto pick the horizon will depend on the type of signal, noise andanomalies that are present in the seismic data.

Although getting the picks of the target horizon can require additionaleffort, this step provides benefits which make it worthwhile. Forexample, quality control can be applied to the static model using thesepicks because the NMO error should not have any surface-consistentcomponent in it. If any surface-consistent components are observed inthe error, the data can be fed back to the static model. Also, thestacking velocity can be calculated from the picks by fitting ahyperbola in the CMP domain and then comparing it to the velocityanalysis results. Any difference between the two velocities wouldindicate an error in either the velocity analysis or the pickingprocess.

FIG. 11 provides a comparison between a shot, the horizon picks and thehyperbolic component of the horizon. It can be seen that the horizonpick and the hyperbolic component of the horizon have the same generaltrend, but differ when there is a sudden change in the event.

After obtaining both the horizon picks and the hyperbolic component, aparameterized non-linear global inversion algorithm was run on each ofthem to estimate the true one-way traveltime operators, as well as thehyperbolic one-way traveltime operators. The Genetic Algorithm (GA) waschosen because it converges very quickly to a satisfying solution.However, as will be apparent to one of ordinary skill in the art, anyinversion algorithm that produces good traveltime operators can be used.

After estimating both sets of operators, the NHC was applied asdescribed above. FIG. 12 shows comparison between a shot before andafter applying NHC. The new shot after NHC is very similar to theoriginal shot except that it doesn't have any sharp changes in theevents, selected ones of which are high-lighted by the arrows. FIG. 13shows the final surface stack after applying the NHC method. FIGS. 14and 15 are comparisons between the stacked image before and after NHCzooming at different parts of the stacks. Specifically, FIG. 14 is acomparison of the stacked image before and after application of the NHCmethod from t=0.8 to 1.5 sec; and FIG. 15 is a comparison of the stackedimage before and after NHC from t=1.6 to 2.3 sec.

Referring now to FIGS. 16 and 17, comparisons between horizon velocityanalyses (HVA) for the target horizon around t=1.05 sec and a secondhorizon around t=1.25 sec before and after NHC are shown.

From the above description, it will be understood that the method of theinvention uses traveltime operators to properly remove the imprint ofburied velocity anomalies that conventional static corrections cannotresolve. The NHC method has advantages over prior art redatumingtechniques, which advantages include the preservation of the referencetime as well as the move-out of the events. In summary, the NHC includesthe following steps:

-   -   a. estimate the stacking velocity as well as the NMO error of a        target horizon;    -   b. estimate two sets of one-way traveltime operators by applying        an inversion algorithm;    -   c. redatum the seismic data with both sets of operators        separately to produce two new datasets;    -   d. combine the causal part from the true operators redatuming        with the anti-causal part from the hyperbolic operators        redatuming to obtain a dataset that does not include the imprint        of the anomalies; and    -   e. redatum back to the surface using the hyperbolic operators.

When the data from surface to the target horizon is redatumed usingthese hyperbolic operators, a new dataset is obtained that is similar tothe CFP redatumed data, except that the anomaly imprint will remain inits location as the causal part of the data and will not shift to theshallower horizons as does the anti-causal part. The results from CFPredatuming and hyperbolic-operator redatuming are similar except in thepart (causal vs. anti-causal) that has the imprints of the anomalies. Bycombining these two clean parts from these two redatuming processes,i.e., the causal part from CFP redatuming and anti-causal part fromhyperbolic-operators redatuming, the method of the invention produces adataset that doesn't have the imprint of the anomaly in either thecausal or the anti-causal part.

As the final step, the data back to the surface is redatumed using thehyperbolic operators which return the hyperbolic move-out of thebehavior without putting back the non-hyperbolic component of theanomaly to any horizon. The result of this process is a dataset that isreferenced to the surface without the anomaly imprint. In accordancewith the method of the invention, all the negative issues with theredatumed data at the target horizon are resolved.

The invention thus applies hyperbolic operators and the combining ofcausal and anti-causal in order to obtain the corrected data set for usein imaging components of different redatuming steps. These two newconcepts provide all of the benefits of CFP redatuming while bothpreserving the shallower data without degradation, as well asreferencing the data back to the surface to preserve the move-outbehavior.

The method of the invention differs from conventional statics solutionsin the following significant aspects: it doesn't assume that velocityanomalies are at the surface; it doesn't assume that velocity anomalieshave low velocities; and it doesn't assume a simple layered earth modelwith vertical ray-paths.

It also differs from conventional redatuming solutions in that itdoesn't require any knowledge about velocity-depth model of the nearsurface; and it requires traveltimes operators only at the targethorizon.

It differs from CFP redatuming in that (a) it preserves the originalacquisition reference of the data; (b) it preserves the hyperbolicmove-out of the data; (c) it preserves the arrival time of the data; and(d) it doesn't degrade the data above the target horizon because ittotally removes the anomaly, rather than merely just shifting it toshallower horizons.

This invention removes the imprint of near surface complexities as wellas buried anomalies from the seismic image while keeping the originalacquisition reference. The most difficult task in this area of seismicdata analysis is properly characterizing the near surface and itsproperties. In the method of the present invention, the only requirementis the total effect of the near surface on the layers below it withoutthe need to know the exact description of that near surface. The methodremoves the total effects of all near-surface and buried anomalies fromthe data and then puts back data relating only to the hyperbolic,smoothly-behaving component of the layers that were removed.

1. A method for improving seismic images by correction of distortions inthe underlying input seismic data caused by a near-surface anomaly thatproduces a non-hyperbolic move-out component of the seismic reflectionbelow the anomaly, the method comprising: a. redatuming the inputseismic data to go from the surface to a target horizon using trueone-way traveltime operators to provide a first new redatuming dataset;b. redatuming the input seismic data using hyperbolic one-way traveltimeoperators to provide a second new redatuming dataset; and c. redatumingthe combination of a first causal part of the first new redatumingdataset and an anti-causal second part of the second redatuming datasetto go from the target horizon back to the surface using hyperbolicone-way traveltime operators, to thereby provide a dataset that isreferenced to the surface without an imprint of the anomaly.
 2. Themethod of claim 1 in which the true one-way traveltime operators arederived from the true two-way traveltime of the target horizon, and thehyperbolic one-way traveltime operators are derived from the hyperboliccomponent of the target horizon.
 3. The method of claim 2 in which thehorizon is selected in the prestack data domain or by stacking velocityanalysis followed by trim statics analysis around the target horizon. 4.The method of claim 1 in which the two sets of true and hyperbolictwo-way traveltimes are converted, respectively, to one-way traveltimeoperators utilizing an inversion algorithm.
 5. The method of claim 4 inwhich the inversion algorithm is a generic algorithm.